limit as x approaches 0 of 2(1+3x)^{2/x}

Lösung

x \to 0 lim (2 (1 + 3 x)^{\frac{2}{x}})

2 e^{6}

Dezimale

806.85758 \dots

Schritte zur Lösung

x \to 0 lim (2 (1 + 3 x)^{\frac{2}{x}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to 0 lim ((1 + 3 x)^{\frac{2}{x}})

Wende Exponentenregel an

= 2 \cdot x \to 0 lim (e^{\frac{2}{x} l n (1 + 3 x)})

Wende die Kettenregel für Grenzen an:

e^{6}

= 2 e^{6}

\frac{d}{d x} (\frac{3 x ^{2} + 2 x}{4 x - 2})

ma c l a u r in ln (3 + x)

\int \frac{1}{x ^{2} x ^{2} - 25} d x

d er i v a t i v e f (x) = 3 sin (x) + 3 cos (x)

s l o p e (- 4, 8), (- 3, 8)